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<a href="_c_svm_derivative_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">//===========================================================================</span><span class="comment"></span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> * </span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> *</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> * \brief       Derivative of a C-SVM hypothesis w.r.t. its hyperparameters.</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> * </span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> * \par</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> * This class provides two main member functions for computing the</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> * derivative of a C-SVM hypothesis w.r.t. its hyperparameters. First,</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * the derivative is prepared in general. Then, the derivative can be</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> * computed comparatively cheaply for any input sample. Needs to be</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> * supplied with pointers to a KernelExpansion and CSvmTrainer.</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * </span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * </span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> *</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * \author      M. Tuma, T. Glasmachers</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * \date        2007-2012</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> *</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> *</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * </span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * </span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published </span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> * </span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span><span class="comment"> * </span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="comment"> *</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="comment"> */</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="comment">//===========================================================================</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span> </div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="preprocessor">#ifndef SHARK_MODELS_CSVMDERIVATIVE_H</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="preprocessor">#define SHARK_MODELS_CSVMDERIVATIVE_H</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="preprocessor">#include &lt;<a class="code" href="_i_nameable_8h.html">shark/Core/INameable.h</a>&gt;</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="preprocessor">#include &lt;<a class="code" href="_i_serializable_8h.html">shark/Core/ISerializable.h</a>&gt;</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span><span class="preprocessor">#include &lt;<a class="code" href="_c_svm_trainer_8h.html">shark/Algorithms/Trainers/CSvmTrainer.h</a>&gt;</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="preprocessor">#include &lt;<a class="code" href="_kernel_expansion_8h.html">shark/Models/Kernels/KernelExpansion.h</a>&gt;</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a> {</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span><span class="comment"></span> </div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span><span class="comment">/// \brief</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span><span class="comment">///</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span><span class="comment">/// This class provides two main member functions for computing the</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span><span class="comment">/// derivative of a C-SVM hypothesis w.r.t. its hyperparameters.</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span><span class="comment">/// The constructor takes a pointer to a KernelClassifier and an SvmTrainer,</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span><span class="comment">/// in the assumption that the former was trained by the latter. It heavily</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span><span class="comment">/// accesses their members to calculate the derivative of the alpha and offset</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span><span class="comment">/// values w.r.t. the SVM hyperparameters, that is, the regularization</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span><span class="comment">/// parameter C and the kernel parameters. This is done in the member function</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="comment">/// prepareCSvmParameterDerivative called by the constructor. After this initial,</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span><span class="comment">/// heavier computation step, modelCSvmParameterDerivative can be called on an</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span><span class="comment">/// input sample to the SVM model, and the method will yield the derivative of</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span><span class="comment">/// the hypothesis w.r.t. the SVM hyperparameters.</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span><span class="comment">///</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span><span class="comment">/// \tparam InputType Same basis type as the kernel expansion&#39;s</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span><span class="comment">/// \tparam CacheType While the basic cache type defaults to float in the QP algorithms, it here defaults to double, because the SVM derivative benefits a lot from higher precision.</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span><span class="comment">///</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span><span class="comment"></span><span class="keyword">template</span>&lt; <span class="keyword">class</span> InputType, <span class="keyword">class</span> CacheType = <span class="keywordtype">double</span> &gt;</div>
<div class="foldopen" id="foldopen00071" data-start="{" data-end="};">
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html">   71</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_c_svm_derivative.html" title="This class provides two main member functions for computing the derivative of a C-SVM hypothesis w....">CSvmDerivative</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_i_serializable.html" title="Abstracts serializing functionality.">ISerializable</a>, <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_i_nameable.html" title="This class is an interface for all objects which can have a name.">INameable</a></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>{</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a7d5c6ca42465fd360c684d5ec3a0d133">   74</a></span>    <span class="keyword">typedef</span> CacheType <a class="code hl_typedef" href="classshark_1_1_c_svm_derivative.html#a7d5c6ca42465fd360c684d5ec3a0d133">QpFloatType</a>;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a9ebe1e82ac4a8d09d74f8aa8db8be056">   75</a></span>    <span class="keyword">typedef</span> <a class="code hl_struct" href="structshark_1_1_kernel_classifier.html" title="Linear classifier in a kernel feature space.">KernelClassifier&lt;InputType&gt;</a> <a class="code hl_typedef" href="classshark_1_1_c_svm_derivative.html#a9ebe1e82ac4a8d09d74f8aa8db8be056">KeType</a>;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a1a954968c2f086b9c7f16b4a68d69556">   76</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_abstract_kernel_function.html" title="Base class of all Kernel functions.">AbstractKernelFunction&lt;InputType&gt;</a> <a class="code hl_typedef" href="classshark_1_1_c_svm_derivative.html#a1a954968c2f086b9c7f16b4a68d69556">KernelType</a>;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a854324eaf0093bae8996e5aa0edc3449">   77</a></span>    <span class="keyword">typedef</span> <a class="code hl_class" href="classshark_1_1_c_svm_trainer.html" title="Training of C-SVMs for binary classification.">CSvmTrainer&lt;InputType, QpFloatType&gt;</a> <a class="code hl_typedef" href="classshark_1_1_c_svm_derivative.html#a854324eaf0093bae8996e5aa0edc3449">TrainerType</a>;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span> </div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span> </div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    <span class="comment">// key external members through which main information is obtained</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a01ce15f34ecda8ecc078af90d254946d">   82</a></span>    <a class="code hl_class" href="classshark_1_1_kernel_expansion.html" title="Linear model in a kernel feature space.">KernelExpansion&lt;InputType&gt;</a>* <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a01ce15f34ecda8ecc078af90d254946d" title="pointer to the KernelExpansion which has to have been been trained by the below SvmTrainer">mep_ke</a>;  <span class="comment">///&lt; pointer to the KernelExpansion which has to have been been trained by the below SvmTrainer</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#ae8a6a9c55b58567e079637463464069d">   83</a></span>    <a class="code hl_class" href="classshark_1_1_c_svm_trainer.html" title="Training of C-SVMs for binary classification.">TrainerType</a>* <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#ae8a6a9c55b58567e079637463464069d" title="pointer to the SvmTrainer with which the above KernelExpansion has to have been trained">mep_tr</a>; <span class="comment">///&lt; pointer to the SvmTrainer with which the above KernelExpansion has to have been trained</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2">   84</a></span>    <a class="code hl_class" href="classshark_1_1_abstract_kernel_function.html">KernelType</a>* <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>; <span class="comment">///&lt; convenience pointer to the underlying kernel function</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a389de13ed64569e21da0f57e42efc39d">   85</a></span>    RealMatrix&amp; <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a389de13ed64569e21da0f57e42efc39d" title="convenience reference to the alpha values of the KernelExpansion">m_alpha</a>; <span class="comment">///&lt; convenience reference to the alpha values of the KernelExpansion</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603">   86</a></span>    <span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;InputType&gt;</a>&amp; <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603" title="convenience reference to the underlying data of the KernelExpansion">m_basis</a>; <span class="comment">///&lt; convenience reference to the underlying data of the KernelExpansion</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#ae64df699b30ae931165780b9e2301ede">   87</a></span>    <span class="keyword">const</span> RealVector&amp; <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#ae64df699b30ae931165780b9e2301ede" title="convenience access to the correction term from the solver, for the rare case that there are no free S...">m_db_dParams_from_solver</a>; <span class="comment">///&lt; convenience access to the correction term from the solver, for the rare case that there are no free SVs</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span> </div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>    <span class="comment">// convenience copies from the CSvmTrainer and the underlying kernel function</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#aa6ebca73981c2e0c5998ad29305dfb71">   90</a></span>    <span class="keywordtype">double</span> <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa6ebca73981c2e0c5998ad29305dfb71" title="the regularization parameter value with which the SvmTrainer trained the KernelExpansion">m_C</a>; <span class="comment">///&lt; the regularization parameter value with which the SvmTrainer trained the KernelExpansion</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a1ee6eca2ca7f7d17fcbd8cb0e9a6838f">   91</a></span>    <span class="keywordtype">bool</span> <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a1ee6eca2ca7f7d17fcbd8cb0e9a6838f" title="is the unconstrained flag of the SvmTrainer set? Influences the derivatives!">m_unconstrained</a>; <span class="comment">///&lt; is the unconstrained flag of the SvmTrainer set? Influences the derivatives!</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64">   92</a></span>    std::size_t <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>; <span class="comment">///&lt; convenience member holding the Number of Kernel Parameters.</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#ac2caaa99a014e8d38e60e17cfec5a9a0">   93</a></span>    std::size_t <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#ac2caaa99a014e8d38e60e17cfec5a9a0" title="convenience member holding the Number of Hyper Parameters.">m_nhp</a>; <span class="comment">///&lt; convenience member holding the Number of Hyper Parameters.</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span> </div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <span class="comment">// information calculated from the KernelExpansion state in the prepareDerivative-step</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9">   96</a></span>    std::size_t <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>; <span class="comment">///&lt; number of free SVs</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449">   97</a></span>    std::size_t <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a>; <span class="comment">///&lt; number of bounded SVs</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a864c7537427ab957fa84672bda0162d4">   98</a></span>    std::vector&lt; std::size_t &gt; <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a864c7537427ab957fa84672bda0162d4" title="indices of free SVs">m_freeAlphaIndices</a>; <span class="comment">///&lt; indices of free SVs</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a1e8289e061e797734a65706b7759a6c0">   99</a></span>    std::vector&lt; std::size_t &gt; <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a1e8289e061e797734a65706b7759a6c0" title="indices of bounded SVs">m_boundedAlphaIndices</a>; <span class="comment">///&lt; indices of bounded SVs</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#afbd0b3dcbf7f6765a08e40bbbf9a145c">  100</a></span>    RealVector <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#afbd0b3dcbf7f6765a08e40bbbf9a145c" title="free non-SV alpha values">m_freeAlphas</a>;    <span class="comment">///&lt; free non-SV alpha values</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a4e241e0dd76c9c4542dbb11215ff27bd">  101</a></span>    RealVector <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a4e241e0dd76c9c4542dbb11215ff27bd" title="bounded non-SV alpha values">m_boundedAlphas</a>; <span class="comment">///&lt; bounded non-SV alpha values</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a9d4715c464f82da4b5be48d18111997e">  102</a></span>    RealVector <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a9d4715c464f82da4b5be48d18111997e" title="labels of bounded non-SVs">m_boundedLabels</a>; <span class="comment">///&lt; labels of bounded non-SVs</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span><span class="comment"></span> </div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span><span class="comment">    /// Main member and result, computed in the prepareDerivative-step:</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span><span class="comment">    /// Stores the derivative of the **free** alphas w.r.t. SVM hyperparameters as obtained</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span><span class="comment">    /// through the CSvmTrainer (for C) and through the kernel (for the kernel parameters).</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span><span class="comment">    /// Each row corresponds to one **free** alpha, each column to one hyperparameter.</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span><span class="comment">    /// The **last** column is the derivative of (free_alphas, b) w.r.t C. All **previous**</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span><span class="comment">    /// columns are w.r.t. the kernel parameters.</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#af618384c52d790cc609ade3a522b38d8">  110</a></span><span class="comment"></span>    RealMatrix <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#af618384c52d790cc609ade3a522b38d8">m_d_alphab_d_theta</a>;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span> </div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span><span class="comment"></span> </div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span><span class="comment">    /// Constructor. Only sets up the main pointers and references to the external instances and data, and</span></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span><span class="comment">    /// performs basic sanity checks.</span></div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span><span class="comment">    /// \param ke pointer to the KernelExpansion which has to have been been trained by the below SvmTrainer</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span><span class="comment">    /// \param trainer pointer to the SvmTrainer with which the above KernelExpansion has to have been trained</span></div>
<div class="foldopen" id="foldopen00118" data-start="{" data-end="}">
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a7ee628c62b706b9b7439840ae5a9546d">  118</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#a7ee628c62b706b9b7439840ae5a9546d">CSvmDerivative</a>( <a class="code hl_struct" href="structshark_1_1_kernel_classifier.html" title="Linear classifier in a kernel feature space.">KeType</a>* <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#aaf377dbac6291d22025ca3c8e92d57d9">ke</a>, <a class="code hl_class" href="classshark_1_1_c_svm_trainer.html" title="Training of C-SVMs for binary classification.">TrainerType</a>* <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#ac11b2f7acd73f07958e8e1d2de9a73a2">trainer</a> )</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    : <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a01ce15f34ecda8ecc078af90d254946d" title="pointer to the KernelExpansion which has to have been been trained by the below SvmTrainer">mep_ke</a>( &amp;<a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#aaf377dbac6291d22025ca3c8e92d57d9">ke</a>-&gt;decisionFunction() ),</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>      <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#ae8a6a9c55b58567e079637463464069d" title="pointer to the SvmTrainer with which the above KernelExpansion has to have been trained">mep_tr</a>( <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#ac11b2f7acd73f07958e8e1d2de9a73a2">trainer</a> ),</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>      <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>( <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#ac11b2f7acd73f07958e8e1d2de9a73a2">trainer</a>-&gt;kernel() ),</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>      <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a389de13ed64569e21da0f57e42efc39d" title="convenience reference to the alpha values of the KernelExpansion">m_alpha</a>( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a01ce15f34ecda8ecc078af90d254946d" title="pointer to the KernelExpansion which has to have been been trained by the below SvmTrainer">mep_ke</a>-&gt;alpha() ),</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>      <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603" title="convenience reference to the underlying data of the KernelExpansion">m_basis</a>( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a01ce15f34ecda8ecc078af90d254946d" title="pointer to the KernelExpansion which has to have been been trained by the below SvmTrainer">mep_ke</a>-&gt;basis() ),</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>      <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#ae64df699b30ae931165780b9e2301ede" title="convenience access to the correction term from the solver, for the rare case that there are no free S...">m_db_dParams_from_solver</a>( <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#ac11b2f7acd73f07958e8e1d2de9a73a2">trainer</a>-&gt;get_db_dParams() ),</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span>      <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa6ebca73981c2e0c5998ad29305dfb71" title="the regularization parameter value with which the SvmTrainer trained the KernelExpansion">m_C</a> ( <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#ac11b2f7acd73f07958e8e1d2de9a73a2">trainer</a>-&gt;C() ),</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>      <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a1ee6eca2ca7f7d17fcbd8cb0e9a6838f" title="is the unconstrained flag of the SvmTrainer set? Influences the derivatives!">m_unconstrained</a>( <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#ac11b2f7acd73f07958e8e1d2de9a73a2">trainer</a>-&gt;isUnconstrained() ),</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>      <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>( <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#ac11b2f7acd73f07958e8e1d2de9a73a2">trainer</a>-&gt;kernel()-&gt;numberOfParameters() ),</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>      <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#ac2caaa99a014e8d38e60e17cfec5a9a0" title="convenience member holding the Number of Hyper Parameters.">m_nhp</a>( <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#ac11b2f7acd73f07958e8e1d2de9a73a2">trainer</a>-&gt;kernel()-&gt;numberOfParameters()+1 )</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>    {</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a01ce15f34ecda8ecc078af90d254946d" title="pointer to the KernelExpansion which has to have been been trained by the below SvmTrainer">mep_ke</a>-&gt;kernel() == <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#ac11b2f7acd73f07958e8e1d2de9a73a2">trainer</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_svm_trainer.html#a084595212c691b938fe6d421f40a908b">kernel</a>(), <span class="stringliteral">&quot;[CSvmDerivative::CSvmDerivative] KernelExpansion and SvmTrainer must use the same KernelFunction.&quot;</span>);</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a01ce15f34ecda8ecc078af90d254946d" title="pointer to the KernelExpansion which has to have been been trained by the below SvmTrainer">mep_ke</a> != NULL, <span class="stringliteral">&quot;[CSvmDerivative::CSvmDerivative] KernelExpansion cannot be NULL.&quot;</span>);</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a01ce15f34ecda8ecc078af90d254946d" title="pointer to the KernelExpansion which has to have been been trained by the below SvmTrainer">mep_ke</a>-&gt;outputShape().numElements() == 1, <span class="stringliteral">&quot;[CSvmDerivative::CSvmDerivative] only defined for binary SVMs.&quot;</span>);</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a01ce15f34ecda8ecc078af90d254946d" title="pointer to the KernelExpansion which has to have been been trained by the below SvmTrainer">mep_ke</a>-&gt;hasOffset() == 1, <span class="stringliteral">&quot;[CSvmDerivative::CSvmDerivative] only defined for SVMs with offset.&quot;</span>);</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a389de13ed64569e21da0f57e42efc39d" title="convenience reference to the alpha values of the KernelExpansion">m_alpha</a>.size2() == 1, <span class="stringliteral">&quot;[CSvmDerivative::CSvmDerivative] this class is only defined for binary SVMs.&quot;</span>);</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        prepareCSvmParameterDerivative(); <span class="comment">//main</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    }</div>
</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span><span class="comment"></span> </div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span><span class="comment">    /// \brief From INameable: return the class name.</span></div>
<div class="foldopen" id="foldopen00139" data-start="{" data-end="}">
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a65fc3c6c7de2ef556fdacaa9376e4acb">  139</a></span><span class="comment"></span>    std::string <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#a65fc3c6c7de2ef556fdacaa9376e4acb" title="From INameable: return the class name.">name</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span><span class="keyword">    </span>{ <span class="keywordflow">return</span> <span class="stringliteral">&quot;CSvmDerivative&quot;</span>; }</div>
</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span> </div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#aaf377dbac6291d22025ca3c8e92d57d9">  142</a></span>    <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code hl_struct" href="structshark_1_1_kernel_classifier.html" title="Linear classifier in a kernel feature space.">KeType</a>* <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#aaf377dbac6291d22025ca3c8e92d57d9">ke</a>() { <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a01ce15f34ecda8ecc078af90d254946d" title="pointer to the KernelExpansion which has to have been been trained by the below SvmTrainer">mep_ke</a>; }</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#ac11b2f7acd73f07958e8e1d2de9a73a2">  143</a></span>    <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code hl_class" href="classshark_1_1_c_svm_trainer.html" title="Training of C-SVMs for binary classification.">TrainerType</a>* <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#ac11b2f7acd73f07958e8e1d2de9a73a2">trainer</a>() { <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#ae8a6a9c55b58567e079637463464069d" title="pointer to the SvmTrainer with which the above KernelExpansion has to have been trained">mep_tr</a>; }</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span><span class="comment"></span> </div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span><span class="comment">    //! Computes the derivative of the model w.r.t. regularization and kernel parameters.</span></div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span><span class="comment">    //! Be sure to call prepareCSvmParameterDerivative after SVM training and before calling this function!</span></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span><span class="comment">    //! \param input an example to be scored by the SVM</span></div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span><span class="comment">    //! \param derivative a vector of derivatives of the score. The last entry is w.r.t. C.</span></div>
<div class="foldopen" id="foldopen00149" data-start="{" data-end="}">
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a2e46e908d670b88e6e5ab32f3482e7d8">  149</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#a2e46e908d670b88e6e5ab32f3482e7d8">modelCSvmParameterDerivative</a>(<span class="keyword">const</span> <a class="code hl_typedef" href="_multi_task_svm_8cpp.html#a0dea9a3a85d327080d9b617903508925">InputType</a>&amp; input, RealVector&amp; derivative )</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>    {</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        <span class="comment">// create temporary batch helpers</span></div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        RealMatrix unit_weights(1,1,1.0);</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>        RealMatrix bof_results(1,1);</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>        <span class="keyword">typename</span> <a class="code hl_struct" href="structshark_1_1_batch.html" title="class which helps using different batch types">Batch&lt;InputType&gt;::type</a> bof_xi = <a class="code hl_struct" href="structshark_1_1_batch.html" title="class which helps using different batch types">Batch&lt;InputType&gt;::createBatch</a>(input,1);</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span>        <span class="keyword">typename</span> <a class="code hl_struct" href="structshark_1_1_batch.html" title="class which helps using different batch types">Batch&lt;InputType&gt;::type</a> bof_input = <a class="code hl_struct" href="structshark_1_1_batch.html" title="class which helps using different batch types">Batch&lt;InputType&gt;::createBatch</a>(input,1);</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>        <a class="code hl_function" href="namespaceshark.html#a1531880b9b4076854b0b26441d353242">getBatchElement</a>(bof_input, 0) = input; <span class="comment">//fixed over entire function scope</span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span> </div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span>        <span class="comment">// init helpers</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span>        RealVector der( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#ac2caaa99a014e8d38e60e17cfec5a9a0" title="convenience member holding the Number of Hyper Parameters.">m_nhp</a> );</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span>        boost::shared_ptr&lt;State&gt; state = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#a9057a4a71b4d28febb171e09bbd22c07" title="Creates an internal state of the kernel.">createState</a>(); <span class="comment">//state from eval and for derivatives</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span>        derivative.resize( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#ac2caaa99a014e8d38e60e17cfec5a9a0" title="convenience member holding the Number of Hyper Parameters.">m_nhp</a> );</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span> </div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span>        <span class="comment">// start calculating derivative</span></div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span>        noalias(derivative) = row(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#af618384c52d790cc609ade3a522b38d8">m_d_alphab_d_theta</a>,<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>); <span class="comment">//without much thinking, we add db/d(\theta) to all derivatives</span></div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>        <span class="comment">// first: go through free SVs and add their contributions (the actual ones, which use the matrix d_alphab_d_theta)</span></div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span>        <span class="keywordflow">for</span> ( std::size_t i=0; i&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>; i++ ) {</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>            <a class="code hl_function" href="namespaceshark.html#a1531880b9b4076854b0b26441d353242">getBatchElement</a>(bof_xi, 0) = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603" title="convenience reference to the underlying data of the KernelExpansion">m_basis</a>.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a864c7537427ab957fa84672bda0162d4" title="indices of free SVs">m_freeAlphaIndices</a>[i]);</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>            <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#abd10e3815efade90c7f9e2a7cc8bcb6c" title="Evaluates the kernel function.">eval</a>( bof_input, bof_xi, bof_results, *state );</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>            <span class="keywordtype">double</span> ker = bof_results(0,0);</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>            <span class="keywordtype">double</span> cur_alpha = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#afbd0b3dcbf7f6765a08e40bbbf9a145c" title="free non-SV alpha values">m_freeAlphas</a>(i);</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>            <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#a48557b9834bc06ccb4e005ce441904c8" title="Computes the gradient of the parameters as a weighted sum over the gradient of all elements of the ba...">weightedParameterDerivative</a>( bof_input, bof_xi, unit_weights, *state, der );</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>            noalias(derivative) += ker * row(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#af618384c52d790cc609ade3a522b38d8">m_d_alphab_d_theta</a>,i); <span class="comment">//for C, simply add up the individual contributions</span></div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>            noalias(subrange(derivative,0,<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>))+= cur_alpha*der;</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        }</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>        <span class="comment">// second: go through all bounded SVs and add their &quot;trivial&quot; derivative contributions</span></div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        <span class="keywordflow">for</span> ( std::size_t i=0; i&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a>; i++ ) {</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>            <a class="code hl_function" href="namespaceshark.html#a1531880b9b4076854b0b26441d353242">getBatchElement</a>(bof_xi, 0) = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603" title="convenience reference to the underlying data of the KernelExpansion">m_basis</a>.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a1e8289e061e797734a65706b7759a6c0" title="indices of bounded SVs">m_boundedAlphaIndices</a>[i]);</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>            <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#abd10e3815efade90c7f9e2a7cc8bcb6c" title="Evaluates the kernel function.">eval</a>( bof_input, bof_xi, bof_results, *state );</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>            <span class="keywordtype">double</span> ker = bof_results(0,0);</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>            <span class="keywordtype">double</span> cur_label = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a9d4715c464f82da4b5be48d18111997e" title="labels of bounded non-SVs">m_boundedLabels</a>(i);</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>            <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#a48557b9834bc06ccb4e005ce441904c8" title="Computes the gradient of the parameters as a weighted sum over the gradient of all elements of the ba...">weightedParameterDerivative</a>( bof_input, bof_xi, unit_weights, *state, der );</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>            derivative( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a> ) += ker * cur_label; <span class="comment">//deriv of bounded alpha w.r.t. C is simply the label</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>            noalias(subrange(derivative,0,<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>))+= cur_label * <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa6ebca73981c2e0c5998ad29305dfb71" title="the regularization parameter value with which the SvmTrainer trained the KernelExpansion">m_C</a> * der;</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        }</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>        <span class="keywordflow">if</span> ( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a1ee6eca2ca7f7d17fcbd8cb0e9a6838f" title="is the unconstrained flag of the SvmTrainer set? Influences the derivatives!">m_unconstrained</a> )</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>            derivative( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a> ) *= <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa6ebca73981c2e0c5998ad29305dfb71" title="the regularization parameter value with which the SvmTrainer trained the KernelExpansion">m_C</a>; <span class="comment">//compensate for log encoding via chain rule</span></div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>            <span class="comment">//(the kernel parameter derivatives are correctly differentiated according to their</span></div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>            <span class="comment">// respective encoding via the kernel&#39;s derivative, so we don&#39;t need to correct for those.)</span></div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span> </div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>        <span class="comment">// in some rare cases, there are no free SVs and we have to manually correct the derivatives using a correcting term from the SvmTrainer.</span></div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        <span class="keywordflow">if</span> ( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a> == 0 ) {</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>            noalias(derivative) += <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#ae64df699b30ae931165780b9e2301ede" title="convenience access to the correction term from the solver, for the rare case that there are no free S...">m_db_dParams_from_solver</a>;</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>        }</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>    }</div>
</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span><span class="comment"></span> </div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span><span class="comment">    //! Whether there are free SVs in the solution. Useful to monitor for degenerate solutions</span></div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span><span class="comment">    //! with only bounded and no free SVs. Be sure to call prepareCSvmParameterDerivative after</span></div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span><span class="comment">    //! SVM training and before calling this function.</span></div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#ad9d1a0937c92a0c506baeeb36df5e2da">  199</a></span><span class="comment"></span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#ad9d1a0937c92a0c506baeeb36df5e2da">hasFreeSVs</a>() { <span class="keywordflow">return</span> ( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a> != 0 ); }<span class="comment"></span></div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span><span class="comment">    //! Whether there are bounded SVs in the solution. Useful to monitor for degenerate solutions</span></div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span><span class="comment">    //! with only bounded and no free SVs. Be sure to call prepareCSvmParameterDerivative after</span></div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span><span class="comment">    //! SVM training and before calling this function.</span></div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a78db48a428319dd6d11d6c592ccd7935">  203</a></span><span class="comment"></span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#a78db48a428319dd6d11d6c592ccd7935">hasBoundedSVs</a>() { <span class="keywordflow">return</span> ( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a> != 0 ); }</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span><span class="comment"></span> </div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span><span class="comment">    /// Access to the matrix of SVM coefficients&#39; derivatives. Derivative w.r.t. C is last.</span></div>
<div class="foldopen" id="foldopen00206" data-start="{" data-end="}">
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#aad1d2282bcb2519f7ff7f31e1a1dc7c2">  206</a></span><span class="comment"></span>    <span class="keyword">const</span> RealMatrix&amp; <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#aad1d2282bcb2519f7ff7f31e1a1dc7c2" title="Access to the matrix of SVM coefficients&#39; derivatives. Derivative w.r.t. C is last.">get_dalphab_dtheta</a>() {</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#af618384c52d790cc609ade3a522b38d8">m_d_alphab_d_theta</a>;</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    }</div>
</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span><span class="comment"></span> </div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span><span class="comment">    /// From ISerializable, reads a network from an archive</span></div>
<div class="foldopen" id="foldopen00211" data-start="{" data-end="}">
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#a4a57799c4b3da25509930d480a0aed19">  211</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#a4a57799c4b3da25509930d480a0aed19" title="From ISerializable, reads a network from an archive.">read</a>( <a class="code hl_typedef" href="namespaceshark.html#ada68729491840669e47c8ad42282424f" title="Type of an archive to read from.">InArchive</a> &amp; archive ) {</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    }<span class="comment"></span></div>
</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span><span class="comment">    /// From ISerializable, writes a network to an archive</span></div>
<div class="foldopen" id="foldopen00214" data-start="{" data-end="}">
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"><a class="line" href="classshark_1_1_c_svm_derivative.html#ab23ece6f8bff1fbfc3820b9c6031a874">  214</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_c_svm_derivative.html#ab23ece6f8bff1fbfc3820b9c6031a874" title="From ISerializable, writes a network to an archive.">write</a>( <a class="code hl_typedef" href="namespaceshark.html#af4f8eb8e9618f5236b71bbcb12b8a524" title="Type of an archive to write to.">OutArchive</a> &amp; archive )<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>    }</div>
</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span> </div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span><span class="comment"></span> </div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span><span class="comment">    ///////////  DERIVATIVE OF BINARY (C-)SVM  ////////////////////</span></div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span><span class="comment"></span><span class="comment"></span> </div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span><span class="comment">    //! Fill m_d_alphab_d_theta, the matrix of derivatives of free SVs w.r.t. C-SVM hyperparameters</span></div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span><span class="comment">    //! as obtained through the CSvmTrainer (for C) and through the kernel (for the kernel parameters).</span></div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span><span class="comment">    //! \par</span></div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span><span class="comment">    //!  Note: we follow the alpha-encoding-conventions of Glasmacher&#39;s dissertation, where the alpha values</span></div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span><span class="comment">    //!  are re-encoded by multiplying each with the corresponding label</span></div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span><span class="comment">    //!</span></div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span><span class="comment"></span>    <span class="keywordtype">void</span> prepareCSvmParameterDerivative() {</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>        <span class="comment">// init convenience size indicators</span></div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>        std::size_t numberOfAlphas = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a389de13ed64569e21da0f57e42efc39d" title="convenience reference to the alpha values of the KernelExpansion">m_alpha</a>.size1();</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span> </div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>        <span class="comment">// first round through alphas: count free and bounded SVs</span></div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        <span class="keywordflow">for</span> ( std::size_t i=0; i&lt;numberOfAlphas; i++ ) {</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>            <span class="keywordtype">double</span> cur_alpha = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a389de13ed64569e21da0f57e42efc39d" title="convenience reference to the alpha values of the KernelExpansion">m_alpha</a>(i,0); <span class="comment">//we assume (and checked) that there is only one class</span></div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>            <span class="keywordflow">if</span> ( cur_alpha != 0.0 ) {</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>                <span class="keywordflow">if</span> ( cur_alpha == <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa6ebca73981c2e0c5998ad29305dfb71" title="the regularization parameter value with which the SvmTrainer trained the KernelExpansion">m_C</a> || cur_alpha == -<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa6ebca73981c2e0c5998ad29305dfb71" title="the regularization parameter value with which the SvmTrainer trained the KernelExpansion">m_C</a> ) { <span class="comment">//the svm formulation using reparametrized alphas is assumed</span></div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>                    <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a1e8289e061e797734a65706b7759a6c0" title="indices of bounded SVs">m_boundedAlphaIndices</a>.push_back(i);</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>                } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>                    <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a864c7537427ab957fa84672bda0162d4" title="indices of free SVs">m_freeAlphaIndices</a>.push_back(i);</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>                }</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>            }</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>        }</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>        <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a> = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a864c7537427ab957fa84672bda0162d4" title="indices of free SVs">m_freeAlphaIndices</a>.size(); <span class="comment">//don&#39;t forget to add b to the count where appropriate</span></div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>        <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a> = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a1e8289e061e797734a65706b7759a6c0" title="indices of bounded SVs">m_boundedAlphaIndices</a>.size();</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>        <span class="comment">// in contrast to the Shark2 implementation, we here don&#39;t store useless constants (i.e., 0, 1, -1), but only the derivs w.r.t. (\alpha_free, b)</span></div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>        <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#af618384c52d790cc609ade3a522b38d8">m_d_alphab_d_theta</a>.resize(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>+1, <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#ac2caaa99a014e8d38e60e17cfec5a9a0" title="convenience member holding the Number of Hyper Parameters.">m_nhp</a>);</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>        <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#af618384c52d790cc609ade3a522b38d8">m_d_alphab_d_theta</a>.clear();</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>        <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a864c7537427ab957fa84672bda0162d4" title="indices of free SVs">m_freeAlphaIndices</a>.push_back( numberOfAlphas ); <span class="comment">//b is always free (but don&#39;t forget to add to count manually)</span></div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span> </div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>        <span class="comment">// 2nd round through alphas: build up the RealVector of free and bounded alphas (needed for matrix-vector-products later)</span></div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>        <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#afbd0b3dcbf7f6765a08e40bbbf9a145c" title="free non-SV alpha values">m_freeAlphas</a>.resize( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>+1);</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>        <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a4e241e0dd76c9c4542dbb11215ff27bd" title="bounded non-SV alpha values">m_boundedAlphas</a>.resize( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a> );</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>        <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a9d4715c464f82da4b5be48d18111997e" title="labels of bounded non-SVs">m_boundedLabels</a>.resize( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a> );</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>        <span class="keywordflow">for</span> ( std::size_t i=0; i&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>; i++ )</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>            <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#afbd0b3dcbf7f6765a08e40bbbf9a145c" title="free non-SV alpha values">m_freeAlphas</a>(i) = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a389de13ed64569e21da0f57e42efc39d" title="convenience reference to the alpha values of the KernelExpansion">m_alpha</a>( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a864c7537427ab957fa84672bda0162d4" title="indices of free SVs">m_freeAlphaIndices</a>[i], 0 );</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>        <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#afbd0b3dcbf7f6765a08e40bbbf9a145c" title="free non-SV alpha values">m_freeAlphas</a>( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a> ) = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a01ce15f34ecda8ecc078af90d254946d" title="pointer to the KernelExpansion which has to have been been trained by the below SvmTrainer">mep_ke</a>-&gt;offset(0);</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>        <span class="keywordflow">for</span> ( std::size_t i=0; i&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a>; i++ ) {</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>            <span class="keywordtype">double</span> cur_alpha = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a389de13ed64569e21da0f57e42efc39d" title="convenience reference to the alpha values of the KernelExpansion">m_alpha</a>( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a1e8289e061e797734a65706b7759a6c0" title="indices of bounded SVs">m_boundedAlphaIndices</a>[i], 0 );</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>            <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a4e241e0dd76c9c4542dbb11215ff27bd" title="bounded non-SV alpha values">m_boundedAlphas</a>(i) = cur_alpha;</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>            <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a9d4715c464f82da4b5be48d18111997e" title="labels of bounded non-SVs">m_boundedLabels</a>(i) = ( (cur_alpha &gt; 0.0) ? 1.0 : -1.0 );</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>        }</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>        </div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>        <span class="comment">//if there are no free support vectors, we are done.</span></div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>        <span class="keywordflow">if</span> ( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a> == 0 ) {</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>            <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>        }</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span> </div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>        <span class="comment">// set up helper variables.</span></div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>        <span class="comment">//      See Tobias Glasmacher&#39;s dissertation, chapter 9.3, for a calculation of the derivatives as well as</span></div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>        <span class="comment">//      for a definition of these variables. -&gt; It&#39;s very easy to follow this code with that chapter open.</span></div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>        <span class="comment">//      The Keerthi-paper &quot;Efficient method for gradient-based...&quot; is also highly recommended for cross-reference.</span></div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>        RealVector der( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a> ); <span class="comment">//derivative storage helper</span></div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>        boost::shared_ptr&lt;State&gt; state = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#a9057a4a71b4d28febb171e09bbd22c07" title="Creates an internal state of the kernel.">createState</a>(); <span class="comment">//state object for derivatives</span></div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span> </div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>        <span class="comment">// create temporary batch helpers</span></div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>        RealMatrix unit_weights(1,1,1.0);</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>        RealMatrix bof_results(1,1);</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>        <span class="keyword">typename</span> Batch&lt;InputType&gt;::type bof_xi;</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>        <span class="keyword">typename</span> Batch&lt;InputType&gt;::type bof_xj;</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>        <span class="keywordflow">if</span> ( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a> != 0 ) {</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>            bof_xi = Batch&lt;InputType&gt;::createBatch( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603" title="convenience reference to the underlying data of the KernelExpansion">m_basis</a>.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a864c7537427ab957fa84672bda0162d4" title="indices of free SVs">m_freeAlphaIndices</a>[0]), 1 ); <span class="comment">//any input works</span></div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>            bof_xj = Batch&lt;InputType&gt;::createBatch( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603" title="convenience reference to the underlying data of the KernelExpansion">m_basis</a>.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a864c7537427ab957fa84672bda0162d4" title="indices of free SVs">m_freeAlphaIndices</a>[0]), 1 ); <span class="comment">//any input works</span></div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>        } <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a> != 0 ) {</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>            bof_xi = Batch&lt;InputType&gt;::createBatch( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603" title="convenience reference to the underlying data of the KernelExpansion">m_basis</a>.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a1e8289e061e797734a65706b7759a6c0" title="indices of bounded SVs">m_boundedAlphaIndices</a>[0]), 1 ); <span class="comment">//any input works</span></div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>            bof_xj = Batch&lt;InputType&gt;::createBatch( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603" title="convenience reference to the underlying data of the KernelExpansion">m_basis</a>.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a1e8289e061e797734a65706b7759a6c0" title="indices of bounded SVs">m_boundedAlphaIndices</a>[0]), 1 ); <span class="comment">//any input works</span></div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>        } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>            <span class="keywordflow">throw</span> <a class="code hl_define" href="_exception_8h.html#a4e03d7dfdfe8cbc90447fa829fc09e4f">SHARKEXCEPTION</a>(<span class="stringliteral">&quot;[CSvmDerivative::prepareCSvmParameterDerivative] Something went very wrong.&quot;</span>);</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>        }</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span> </div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>        </div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>        <span class="comment">// initialize H and dH</span></div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>        <span class="comment">//H is the the matrix </span></div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>        <span class="comment">//H = (K 1; 1 0)</span></div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>        <span class="comment">// where the ones are row or column vectors and 0 is a scalar.</span></div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>        <span class="comment">// K is the kernel matrix spanned by the free support vectors</span></div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>        RealMatrix H( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a> + 1, <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a> + 1,0.0);</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>        std::vector&lt; RealMatrix &gt; dH( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a> , RealMatrix(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>+1, <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>+1));</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span>        <span class="keywordflow">for</span> ( std::size_t i=0; i&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>; i++ ) {</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>            <a class="code hl_function" href="namespaceshark.html#a1531880b9b4076854b0b26441d353242">getBatchElement</a>(bof_xi, 0) = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603" title="convenience reference to the underlying data of the KernelExpansion">m_basis</a>.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a864c7537427ab957fa84672bda0162d4" title="indices of free SVs">m_freeAlphaIndices</a>[i]); <span class="comment">//fixed over outer loop</span></div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>            <span class="comment">// fill the off-diagonal entries..</span></div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>            <span class="keywordflow">for</span> ( std::size_t j=0; j&lt;i; j++ ) {</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>                <a class="code hl_function" href="namespaceshark.html#a1531880b9b4076854b0b26441d353242">getBatchElement</a>(bof_xj, 0) = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603" title="convenience reference to the underlying data of the KernelExpansion">m_basis</a>.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a864c7537427ab957fa84672bda0162d4" title="indices of free SVs">m_freeAlphaIndices</a>[j]); <span class="comment">//get second sample into a batch</span></div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span>                <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#abd10e3815efade90c7f9e2a7cc8bcb6c" title="Evaluates the kernel function.">eval</a>( bof_xi, bof_xj, bof_results, *state );</div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span>                H( i,j ) = H( j,i ) = bof_results(0,0);</div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span>                <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#a48557b9834bc06ccb4e005ce441904c8" title="Computes the gradient of the parameters as a weighted sum over the gradient of all elements of the ba...">weightedParameterDerivative</a>( bof_xi, bof_xj, unit_weights, *state, der );</div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span>                <span class="keywordflow">for</span> ( std::size_t k=0; k&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>; k++ ) {</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>                    dH[k]( i,j ) = dH[k]( j,i ) = der(k);</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>                }</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>            }</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>            <span class="comment">// ..then fill the diagonal entries..</span></div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>            <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#abd10e3815efade90c7f9e2a7cc8bcb6c" title="Evaluates the kernel function.">eval</a>( bof_xi, bof_xi, bof_results, *state );</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>            H( i,i ) = bof_results(0,0);</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>            H( i, <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>) = H( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>, i) = 1.0;</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>            <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#a48557b9834bc06ccb4e005ce441904c8" title="Computes the gradient of the parameters as a weighted sum over the gradient of all elements of the ba...">weightedParameterDerivative</a>( bof_xi, bof_xi, unit_weights, *state, der );</div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>            <span class="keywordflow">for</span> ( std::size_t k=0; k&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>; k++ ) {</div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>                dH[k]( i,i ) = der(k);</div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>            }</div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>            <span class="comment">// ..and finally the last row/column (pertaining to the offset parameter b)..</span></div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>            <span class="keywordflow">for</span> (std::size_t k=0; k&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>; k++)</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>                dH[k]( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>, i ) = dH[k]( i, <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a> ) = 0.0;</div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>        }</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span> </div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>        <span class="comment">// ..the lower-right-most entry gets set separately:</span></div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>        <span class="keywordflow">for</span> ( std::size_t k=0; k&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>; k++ ) {</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>            dH[k]( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>, <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a> ) = 0.0;</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>        }</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>        </div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>        <span class="comment">// initialize R and dR</span></div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>        RealMatrix R( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>+1, <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a> );</div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>        std::vector&lt; RealMatrix &gt; dR( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>, RealMatrix(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>+1, <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a>));</div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>        <span class="keywordflow">for</span> ( std::size_t i=0; i&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a>; i++ ) {</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>            <a class="code hl_function" href="namespaceshark.html#a1531880b9b4076854b0b26441d353242">getBatchElement</a>(bof_xi, 0) = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603" title="convenience reference to the underlying data of the KernelExpansion">m_basis</a>.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a1e8289e061e797734a65706b7759a6c0" title="indices of bounded SVs">m_boundedAlphaIndices</a>[i]); <span class="comment">//fixed over outer loop</span></div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>            <span class="keywordflow">for</span> ( std::size_t j=0; j&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>; j++ ) { <span class="comment">//this time, we (have to) do it row by row</span></div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>                <a class="code hl_function" href="namespaceshark.html#a1531880b9b4076854b0b26441d353242">getBatchElement</a>(bof_xj, 0) = <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa37ffb53e952460a43a53f66d2483603" title="convenience reference to the underlying data of the KernelExpansion">m_basis</a>.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a864c7537427ab957fa84672bda0162d4" title="indices of free SVs">m_freeAlphaIndices</a>[j]); <span class="comment">//get second sample into a batch</span></div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>                <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#abd10e3815efade90c7f9e2a7cc8bcb6c" title="Evaluates the kernel function.">eval</a>( bof_xi, bof_xj, bof_results, *state );</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>                R( j,i ) = bof_results(0,0);</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>                <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a8e58aaf2f55f175568cf51728c5c86f2" title="convenience pointer to the underlying kernel function">mep_k</a>-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#a48557b9834bc06ccb4e005ce441904c8" title="Computes the gradient of the parameters as a weighted sum over the gradient of all elements of the ba...">weightedParameterDerivative</a>( bof_xi, bof_xj, unit_weights, *state, der );</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>                <span class="keywordflow">for</span> ( std::size_t k=0; k&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>; k++ )</div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>                    dR[k]( j,i ) = der(k);</div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span>            }</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>            R( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>, i ) = 1.0; <span class="comment">//last row is for b</span></div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span>            <span class="keywordflow">for</span> ( std::size_t k=0; k&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>; k++ )</div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span>                dR[k]( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aad32ca8b5eaae5c0c00f46f05c1891d9" title="number of free SVs">m_noofFreeSVs</a>, i ) = 0.0;</div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span>        }</div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span>        </div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span>        </div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span>        <span class="comment">//O.K.: A big step of the computation of the derivative m_d_alphab_d_theta is</span></div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span>        <span class="comment">// the multiplication with H^{-1} B. (where B are the other terms).</span></div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>        <span class="comment">// However  instead of storing m_d_alphab_d_theta_i = -H^{-1}*b_i</span></div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>        <span class="comment">//we store _i and compute the multiplication with the inverse</span></div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>        <span class="comment">//afterwards by solving the system Hx_i = b_i </span></div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>        <span class="comment">//for i = 1....m_nkp+1</span></div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>        <span class="comment">//this is a lot faster and numerically more stable.</span></div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span> </div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>        <span class="comment">// compute the derivative of (\alpha, b) w.r.t. C</span></div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>        <span class="keywordflow">if</span> ( <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a> &gt; 0 ) {</div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span>            noalias(column(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#af618384c52d790cc609ade3a522b38d8">m_d_alphab_d_theta</a>,<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>)) = prod( R, <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a9d4715c464f82da4b5be48d18111997e" title="labels of bounded non-SVs">m_boundedLabels</a>);</div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>        }</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>        <span class="comment">// compute the derivative of (\alpha, b) w.r.t. the kernel parameters</span></div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span>        <span class="keywordflow">for</span> ( std::size_t k=0; k&lt;<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#aa71919c545c490a4677bd05a78d6ad64" title="convenience member holding the Number of Kernel Parameters.">m_nkp</a>; k++ ) {</div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span>            RealVector sum = prod( dH[k], <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#afbd0b3dcbf7f6765a08e40bbbf9a145c" title="free non-SV alpha values">m_freeAlphas</a> ); <span class="comment">//sum = dH * \alpha_f</span></div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>            <span class="keywordflow">if</span>(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a313f8373d924b205dd5d6c9720a29449" title="number of bounded SVs">m_noofBoundedSVs</a> &gt; 0)</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>                noalias(sum) += prod( dR[k], <a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#a4e241e0dd76c9c4542dbb11215ff27bd" title="bounded non-SV alpha values">m_boundedAlphas</a> ); <span class="comment">// sum += dR * \alpha_r , i.e., the C*y_g is expressed as alpha_g</span></div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>            <span class="comment">//fill the remaining columns of the derivative matrix (except the last, which is for C)</span></div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>            noalias(column(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#af618384c52d790cc609ade3a522b38d8">m_d_alphab_d_theta</a>,k)) = sum;</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>        }</div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>        </div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>        <span class="comment">//lastly solve the system Hx_i = b_i </span></div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>        <span class="comment">// MAJOR STEP: this is the achilles heel of the current implementation, cf. keerthi 2007</span></div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>        <span class="comment">// TODO: mtq: explore ways for speed-up..</span></div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>        <span class="comment">//compute via moore penrose pseudo-inverse</span></div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>        noalias(<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#af618384c52d790cc609ade3a522b38d8">m_d_alphab_d_theta</a>) = - solveH(H,<a class="code hl_variable" href="classshark_1_1_c_svm_derivative.html#af618384c52d790cc609ade3a522b38d8">m_d_alphab_d_theta</a>);</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>        </div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>        <span class="comment">// that&#39;s all, folks; we&#39;re done.</span></div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span>    }</div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>    </div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>    RealMatrix solveH(RealMatrix <span class="keyword">const</span>&amp; H, RealMatrix <span class="keyword">const</span>&amp; rhs){</div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>        <span class="comment">//implement using moore penrose pseudo inverse</span></div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>        RealMatrix HTH=prod(trans(H),H);</div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>        RealMatrix result = solve(HTH,prod(H,rhs),blas::symm_semi_pos_def(),blas::left());</div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>        <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>    }</div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>};<span class="comment">//class</span></div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span> </div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span> </div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>}<span class="comment">//namespace</span></div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span><span class="preprocessor">#endif</span></div>
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